Chaos-Based Signal Processing

Given a time series measured (or generated) by a known or an unknown dynamical system we address a series of problems which can be considered as advanced signal processing tasks, namely: (1) section-wise approximation of the measured signal by pieces of trajectories from a chosen nonlinear dynamical system (model); (2) signal restoration when the measured signal has been corrupted e.g. by quantization; (3) signal coding and compression. These tasks can be addressed using a new approach to the shadowing problem based on nonlinear observability problem. Its goal is to reproduce initial conditions for a dynamical system under consideration (approximating waveform generator) giving rise to an orbit which is optimal in the sense of average distance from the measured (or prescribed) transient output waveform. We present the results obtained using the Chua’s circuit as approximating waveform generator.